A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Comprehensive secondary pyrolysis in fluidized-bed fast pyrolysis of biomass, a fluid dynamics based modelling effort

Homogenous secondary pyrolysis is category of reactions following the primary pyrolysis and presumed important for fast pyrolysis. For the comprehensive chemistry and fluid dynamics, a probability density functional (PDF) approach is used; with a kinetic scheme comprising 134 species and 4169 reactions being implemented. With aid of acceleration techniques, most importantly Dimension Reduction, Chemistry Agglomeration and In-situ Tabulation (ISAT), a solution within reasonable time was obtained. More work is required; however, a solution for levoglucosan (C6H10O5) being fed through the inlet with fluidizing gas at 500 °C, has been obtained. 88.6% of the levoglucosan remained non-decomposed, and 19 different decomposition product species were found above 0.01% by weight. A homogenous secondary pyrolysis scheme proposed can thus be implemented in a CFD environment and acceleration techniques can speed-up the calculation for application in engineering settings.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

Laminar-turbulent transition in Raman fiber lasers:a first passage statistics based analysis

Loss of coherence with increasing excitation amplitudes and spatial size modulation is a fundamental problem in designing Raman fiber lasers. While it is known that ramping up laser pump power increases the amplitude of stochastic excitations, such higher energy inputs can also lead to a transition from a linearly stable coherent laminar regime to a non-desirable disordered turbulent state. This report presents a new statistical methodology, based on first passage statistics, that classifies lasing regimes in Raman fiber lasers, thereby leading to a fast and highly accurate identification of a strong instability leading to a laminar-turbulent phase transition through a self-consistently defined order parameter. The results have been consistent across a wide range of pump power values, heralding a breakthrough in the non-invasive analysis of fiber laser dynamics.

Improved stochastic optimization of railway timetables

We present a general model to find the best allocation of a limited amount of supplements (extra minutes added to a timetable in order to reduce delays) on a set of interfering railway lines. By the best allocation, we mean the solution under which the weighted sum of expected delays is minimal. Our aim is to finely adjust an already existing and well-functioning timetable. We model this inherently stochastic optimization problem by using two-stage recourse models from stochastic programming, building upon earlier research from the literature. We present an improved formulation, allowing for an efficient solution using a standard algorithm for recourse models. We show that our model may be solved using any of the following theoretical frameworks: linear programming, stochastic programming and convex non-linear programming, and present a comparison of these approaches based on a real-life case study. Finally, we introduce stochastic dependency into the model, and present a statistical technique to estimate the model parameters from empirical data.

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Hydrological dynamics between a coastal aquifer and the adjacent estuarine system, Biscayne Bay, South Florida

Geochemical and geophysical approaches have been used to investigate the freshwater and saltwater dynamics in the coastal Biscayne Aquifer and Biscayne Bay. Stable isotopes of oxygen and hydrogen, and concentrations of Sr2+ and Ca2+ were combined in two geochemical mixing models to provide estimates of the various freshwater inputs (precipitation, canal water, and groundwater) to Biscayne Bay and the coastal canal system in South Florida. Shallow geophysical electromagnetic and direct current resistivity surveys were used to image the geometry and stratification of the saltwater mixing zone in the near coastal (less than 1km inland) Biscayne Aquifer. The combined stable isotope and trace metal models suggest a ratio of canal input-precipitation-groundwater of 38%–52%–10% in the wet season and 37%–58%–5% in the dry season with an error of 25%, where most (20%) of the error was attributed to the isotope regression model, while the remaining 5% error was attributed to the Sr2+/Ca2+ mixing model. These models suggest rainfall is the dominate source of freshwater to Biscayne Bay. For a bay-wide water budget that includes saltwater and freshwater mixing, fresh groundwater accounts for less than 2% of the total input. A similar Sr 2+/Ca2+ tracer model indicates precipitation is the dominate source in 9 out of 10 canals that discharge into Biscayne Bay. The two-component mixing model converged for 100% of the freshwater canal samples in this study with 63% of the water contributed to the canals coming from precipitation and 37% from groundwater inputs ±4%. There was a seasonal shift from 63% precipitation input in the dry season to 55% precipitation input in the wet season. The three end-member mixing model converged for only 60% of the saline canal samples possibly due to non-conservative behavior of Sr2+ and Ca2+ in saline groundwater discharging into the canal system. Electromagnetic and Direct Current resistivity surveys were successful at locating and estimating the geometry and depth of the freshwater/saltwater interface in the Biscayne Aquifer at two near coastal sites. A saltwater interface that deepened as the survey moved inland was detected with a maximum interpreted depth to the interface of 15 meters, approximately 0.33 km inland from the shoreline. ^

A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^

Turkey and neo-Ottomanism: Domestic sources, dynamics and foreign policy

This study examined the relationship between the Turkish Islamic movements and the present government of the Justice and Development Party ( Adalet ve Kalkinma Partisi, AK Party). Since the AK Party came to power in 2002 it implemented unparalleled political reforms and pursued to improve Turkey’s relations with the EU. Opponents argued that because of the dominance of the secular military in Turkish politics, the AK Party is forced to secretly advance its Islamic agenda using the language and symbolism of democracy and human rights. This study argued that the ideas of the AK Party show similarities with the “Ottomanist” thought of the late Ottoman era. With special reference to the preservation of the Ottoman State, Ottomanism in an eclectic way was able to incorporate Islamic principles like freedom, justice and consultation into the political arena which was increasingly dominated by the secular European concepts. Literature on Islam and politics in Turkey, however, disregards the Ottoman roots of freedom and pluralism and tends to reduce the relationship between religion and state into exclusively confrontational struggles. This conceptualization of the political process relies on particular non-Turkish Muslim experiences which do not necessarily represent Islam’s venture in Turkey. Contrary to the prevailing scholarship, Islamic movements in Turkey, namely, Naqshbandi, National View and Nur, which are discussed in detail in this study, are not monolithic. They all uphold the same creedal tenets of Islam but they have sharp differences in terms of how they conceptualize the role of religious agency in politics. I argue that this diversity is a result of three distinct methodologies of Islamic religious life which are the Tariqah (Tarikat ), Shariah (Şeriat), and Haqiqah ( Hakikat). The differences between these three approaches represent a typological hierarchy in the formation of the Muslim/believer as an agent of Islamic identity. Through these different if not conflicting modes, the AK Party reconnected itself with Turkey’s Ottoman heritage in a post-Ottoman, secular setting and was able to develop an eclectic political identity of Neo-Ottomanism that is evident in the flexibility if not inconsistency of its domestic and foreign policy preferences.

Diel Patterns of Patch Reef Community Dynamics in a Caribbean Back-Reef System

Back-reef seascapes represent critical habitat for juvenile and adult fishes. Patch reef, seagrass, and mangrove habitats form a heterogeneous mosaic, often linked by species that use reefs as structure during the day and make foraging migrations into soft-bottom habitat at night. Artificial reefs are used to model natural patch reefs, however may not function equivalently as fish habitat. To study the relative value of natural and artificial patch reefs as fish habitat, these communities in the Sea of Abaco, Bahamas were compared using roving diver surveys and time-lapse photography. Diel turnover in fish abundance, recorded with time-lapse photography and illuminated by infrared light, was quantified across midday, dusk, and night periods to explore possible effects of reef type (artificial vs. natural) on these patterns. Diurnal communities on natural reefs exhibited greater fish abundance, species richness, and functional diversity compared to artificial reefs. Furthermore, both types of reef communities exhibited a significant shift across the diel period, characterized by a decline in total fish density at night, especially for grunts (Haemulidae). Cross-habitat foraging migrations by diurnal or nocturnal species, such as haemulids, are likely central drivers of this twilight turnover and can represent important energy and nutrient subsidies. Time-lapse surveys provided more consistent measures of reef fish assemblages for the smaller artificial reef habitats, yet underestimated abundance of certain taxa and species richness on larger patch habitats when compared to the roving diver surveys. Time-lapse photography complemented with infrared light represent a valuable non-invasive approach to studying behavior of focal species and their fine-scale temporal dynamics in shallow-reef communities.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Factors Affecting Current and Future Treeline Locations and Dynamics in the Peruvian Andes

The elevational distributions of tropical treelines are thought to be determined by temperature, and are predicted to shift upslope in response to global warming. In contrast to this hypothesis, global-scale studies have shown that only half of all studied treelines are shifting upslope. Understanding how treelines will respond to climate change has important implications for global biodiversity, especially in the tropics, because tropical treelines generally represent the upper-elevation distribution limit of the hyper-diverse cloudforest ecosystem. In Chapter 1, I introduce the idea that grasslands found above tropical treelines may represent a potential grass ceiling which forest species cannot cross or invade. I use an extensive literature review to outline potential mechanisms which may be acting to stabilize treeline and prevent forest expansion into high-elevation grasslands. In Chapters 2-4, I begin to explore these potential mechanisms through the use of observational and experimental methods. In Chapter 2, I show that there are significant numbers of seedlings occurring just outside of the treeline in the open grasslands and that seed rain is unlikely to limit seedling recruitment above treeline. I also show that microclimates outside of the closed-canopy cloudforest are highly variable and that mean temperatures are likely a poor explanation of tropical treeline elevations. In Chapter 3, I show that juvenile trees maintain freezing resistances similar to adults, but nighttime radiative cooling near the ground in the open grassland results in lower cold temperatures relative to the free atmosphere, exposing seedlings of some species growing above treeline to lethal frost events. In Chapter 4, I use a large-scale seedling transplant experiment to test the effects of mean temperature, absolute low temperature and shade on transplanted seedling survival. I find that increasing mean temperature negatively affects seedling survival of two treeline species while benefiting another. In addition, low temperature extremes and the presence of shade also appear to be important factors affecting seedling survival above tropical treelines. This work demonstrates that mean temperature is a poor predictor of tropical treelines and that temperature extremes, especially low temperatures, and non-climatic variables should be included in predictions of current and future tropical treeline dynamics.

Turkey and Neo-Ottomanism: Domestic Sources, Dynamics and Foreign Policy

This study examined the relationship between the Turkish Islamic movements and the present government of the Justice and Development Party (Adalet ve Kalkinma Partisi, AK Party). Since the AK Party came to power in 2002 it implemented unparalleled political reforms and pursued to improve Turkey’s relations with the EU. Opponents argued that because of the dominance of the secular military in Turkish politics, the AK Party is forced to secretly advance its Islamic agenda using the language and symbolism of democracy and human rights. This study argued that the ideas of the AK Party show similarities with the “Ottomanist” thought of the late Ottoman era. With special reference to the preservation of the Ottoman State, Ottomanism in an eclectic way was able to incorporate Islamic principles like freedom, justice and consultation into the political arena which was increasingly dominated by the secular European concepts. Literature on Islam and politics in Turkey, however, disregards the Ottoman roots of freedom and pluralism and tends to reduce the relationship between religion and state into exclusively confrontational struggles. This conceptualization of the political process relies on particular non-Turkish Muslim experiences which do not necessarily represent Islam’s venture in Turkey. Contrary to the prevailing scholarship, Islamic movements in Turkey, namely, Naqshbandi, National View and Nur, which are discussed in detail in this study, are not monolithic. They all uphold the same creedal tenets of Islam but they have sharp differences in terms of how they conceptualize the role of religious agency in politics. I argue that this diversity is a result of three distinct methodologies of Islamic religious life which are the Tariqah (Tarikat), Shariah (Şeriat), and Haqiqah (Hakikat). The differences between these three approaches represent a typological hierarchy in the formation of the Muslim/believer as an agent of Islamic identity. Through these different if not conflicting modes, the AK Party reconnected itself with Turkey’s Ottoman heritage in a post-Ottoman, secular setting and was able to develop an eclectic political identity of Neo-Ottomanism that is evident in the flexibility if not inconsistency of its domestic and foreign policy preferences.